Problem: Solve for $x$ and $y$ using elimination. ${-x+4y = 25}$ ${4x+3y = 33}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $4$ ${-4x+16y = 100}$ $4x+3y = 33$ Add the top and bottom equations together. $19y = 133$ $\dfrac{19y}{{19}} = \dfrac{133}{{19}}$ ${y = 7}$ Now that you know ${y = 7}$ , plug it back into $\thinspace {-x+4y = 25}\thinspace$ to find $x$ ${-x + 4}{(7)}{= 25}$ $-x+28 = 25$ $-x+28{-28} = 25{-28}$ $-x = -3$ $\dfrac{-x}{{-1}} = \dfrac{-3}{{-1}}$ ${x = 3}$ You can also plug ${y = 7}$ into $\thinspace {4x+3y = 33}\thinspace$ and get the same answer for $x$ : ${4x + 3}{(7)}{= 33}$ ${x = 3}$